Integrability of Hamiltonians with polynomial potentials

In this work, we study dynamical systems with polynomial potentials—such as those of Henon–Heiles, Yang–Mills and various generalizations—by means of the nonintegrability theory developed by the authors. All these problems have also been investigated by using other theories like those proposed by Ziglin, Yoshida, Morales or the Painlevé analysis. In the examples considered, our method allows us to reproduce with quite less work or even to improve the results obtained by other authors.